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| 07/24/2006 04:28 PM by name withheld; alternating coordination game |
This is an alternating coordination game. To check whether (Y, Y) is an SPNE, we need to know weather the players have incentive to deviate from Y. Suppose (Y, Y) is an SPNE. Then payoff for each player is 1/ (1-delta), where delta is the discount factor. If one player deviates to X and possibly the equilibrium will switch to (X, X), the payoff for each player is 0+delta*[2/ (1-delta)]. If 0+ delta*[2/ (1-delta)]> 1/ (1-delta), that is delta>1/2, then players have incentive to deviate to X and (Y, Y) is not an SPNE.
Consider player 1’s situation at period 0, if he or she chooses X, the possible equilibrium is (X, X) and payoff is 2/ (1-delta). If he or she chooses Y and delta<1/2, the possible equilibrium is (Y, Y) and payoff is 1/ (1-delta). If he or she chooses Y and delta>1/2, the possible equilibrium is still (X, X) and payoff is 0+ delta*[2/ (1-delta)] because the players mismatch at the first period and switch back to (X, X) from period 2. Clearly, at period 0, player 1 will choose X and (X, X) is the only possible SPNE. [Manage messages]
| 07/23/2006 02:08 AM by Stella; alternating moves game |
Can you pls help me with this question? consider the alternating moves game where in period 0 player 1 chooses an action which she carries out in period 1, subsequently in every odd period player 2 chooses an action, and in every even [View full text and thread]
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